Question

An object of mass 10 kg Is released from rest in a liquld. If the object moves a distance of 2 m while sinking In time duration of 1 s, then the mass of the Ilquld displaced by the submerged object Is (Acceleration due to gravity = 10 m s$^{-2}$)

• A. 5 kg
• B. 6 kg
• C. 3 kg
• D. 4 kg

Answer 1

Answer: (B)

6 kg

Answer 2

1. Calculate Acceleration: Using the kinematic equation $s = ut + \frac{1}{2}at^2$ with $s=2$ m, $u=0$ m/s, and $t=1$ s, we find the acceleration $a = 4$ m/s².

2. Force Analysis: The forces acting on the object are its weight ($W = m_{obj}g$) downwards, the buoyant force ($B = m_{disp}g$) upwards, and the drag force ($F_d$) upwards, opposing motion.

3. Newton's Second Law: Applying $F_{net} = m_{obj}a$, we get $m_{obj}g - m_{disp}g - F_d = m_{obj}a$.

4. Solve for Displaced Mass: Substituting values ($m_{obj}=10$ kg, $g=10$ m/s², $a=4$ m/s²), we have $100 - 10m_{disp} - F_d = 40$. This simplifies to $10m_{disp} + F_d = 60$. Assuming $F_d=0$ (as no information about drag is given), we get $10m_{disp} = 60$, yielding $m_{disp} = 6$ kg.